test: Added matrix-test for testing projective transform accuracy

This test uses __float128 data type when it is available
for implementing a "perfect" reference implementation. The
output from from pixman_transform_point_31_16() and
pixman_transform_point_31_16_affine() is compared with the
reference implementation to make sure that the rounding
errors may only show up in a single least significant bit.

The platforms and compilers, which do not support __float128
data type, can rely on crc32 checksum for the pseudorandom
transform results.

2 files changed, 187 insertions, 0 deletions

diff --git a/test/Makefile.sources b/test/Makefile.sources
index 8c0b505..e323a8e 100644
--- a/test/Makefile.sources
+++ b/test/Makefile.sources
@@ -17,6 +17,7 @@ TESTPROGRAMS =			\
 	gradient-crash-test	\
 	region-contains-test	\
 	alphamap		\
+	matrix-test		\
 	stress-test		\
 	composite-traps-test	\
 	blitters-test		\
diff --git a/test/matrix-test.c b/test/matrix-test.c
new file mode 100644
index 0000000..8437dd2
--- /dev/null
+++ b/test/matrix-test.c
@@ -0,0 +1,186 @@
+/*
+ * Copyright © 2012 Siarhei Siamashka <siarhei.siamashka@gmail.com>
+ *
+ * Permission is hereby granted, free of charge, to any person obtaining a
+ * copy of this software and associated documentation files (the "Software"),
+ * to deal in the Software without restriction, including without limitation
+ * the rights to use, copy, modify, merge, publish, distribute, sublicense,
+ * and/or sell copies of the Software, and to permit persons to whom the
+ * Software is furnished to do so, subject to the following conditions:
+ *
+ * The above copyright notice and this permission notice (including the next
+ * paragraph) shall be included in all copies or substantial portions of the
+ * Software.
+ *
+ * THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
+ * IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
+ * FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT.  IN NO EVENT SHALL
+ * THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
+ * LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING
+ * FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER
+ * DEALINGS IN THE SOFTWARE.
+ */
+
+#include "utils.h"
+#include <assert.h>
+#include <stdlib.h>
+#include <stdio.h>
+#include <math.h>
+
+#ifdef HAVE_FLOAT128
+
+#define pixman_fixed_to_float128(x) (((__float128)(x)) / 65536.0Q)
+
+typedef struct { __float128 v[3]; } pixman_vector_f128_t;
+typedef struct { __float128 m[3][3]; } pixman_transform_f128_t;
+
+pixman_bool_t
+pixman_transform_point_f128 (const pixman_transform_f128_t *t,
+                             const pixman_vector_f128_t    *v,
+                             pixman_vector_f128_t          *result)
+{
+    int i;
+    for (i = 0; i < 3; i++)
+    {
+        result->v[i] = t->m[i][0] * v->v[0] +
+                       t->m[i][1] * v->v[1] +
+                       t->m[i][2] * v->v[2];
+    }
+    if (result->v[2] != 0)
+    {
+        result->v[0] /= result->v[2];
+        result->v[1] /= result->v[2];
+        result->v[2] = 1;
+        return TRUE;
+    }
+    else
+    {
+        return FALSE;
+    }
+}
+
+pixman_bool_t does_it_fit_fixed_48_16 (__float128 x)
+{
+    if (x >= 65536.0Q * 65536.0Q * 32768.0Q)
+        return FALSE;
+    if (x <= -65536.0Q * 65536.0Q * 32768.0Q)
+        return FALSE;
+    return TRUE;
+}
+
+#endif
+
+uint32_t
+test_matrix (int testnum, int verbose)
+{
+    uint32_t crc32 = 0;
+    int i, j, k;
+    pixman_bool_t is_affine;
+
+    prng_srand (testnum);
+
+    for (i = 0; i < 100; i++)
+    {
+        pixman_bool_t           transform_ok;
+        pixman_transform_t      ti;
+        pixman_vector_48_16_t   vi, result_i;
+#ifdef HAVE_FLOAT128
+        pixman_transform_f128_t tf;
+        pixman_vector_f128_t    vf, result_f;
+#endif
+        prng_randmemset (&ti, sizeof(ti), 0);
+        prng_randmemset (&vi, sizeof(vi), 0);
+
+        for (j = 0; j < 3; j++)
+        {
+            /* make sure that "vi" contains 31.16 fixed point data */
+            vi.v[j] >>= 17;
+            /* and apply random shift */
+            if (prng_rand_n (3) == 0)
+                vi.v[j] >>= prng_rand_n (46);
+        }
+
+        if (prng_rand_n (2))
+        {
+            /* random shift for the matrix */
+            for (j = 0; j < 3; j++)
+                for (k = 0; k < 3; k++)
+                    ti.matrix[j][k] >>= prng_rand_n (30);
+        }
+
+        if (prng_rand_n (2))
+        {
+            /* affine matrix */
+            ti.matrix[2][0] = 0;
+            ti.matrix[2][1] = 0;
+            ti.matrix[2][2] = pixman_fixed_1;
+        }
+
+        if (prng_rand_n (2))
+        {
+            /* cartesian coordinates */
+            vi.v[2] = pixman_fixed_1;
+        }
+
+        is_affine = (ti.matrix[2][0] == 0 && ti.matrix[2][1] == 0 &&
+                     ti.matrix[2][2] == pixman_fixed_1 &&
+                     vi.v[2] == pixman_fixed_1);
+
+        transform_ok = TRUE;
+        if (is_affine && prng_rand_n (2))
+            pixman_transform_point_31_16_affine (&ti, &vi, &result_i);
+        else
+            transform_ok = pixman_transform_point_31_16 (&ti, &vi, &result_i);
+
+        crc32 = compute_crc32 (crc32, &result_i, sizeof(result_i));
+
+#ifdef HAVE_FLOAT128
+        /* compare with a reference 128-bit floating point implementation */
+        for (j = 0; j < 3; j++)
+        {
+            vf.v[j] = pixman_fixed_to_float128 (vi.v[j]);
+            for (k = 0; k < 3; k++)
+            {
+                tf.m[j][k] = pixman_fixed_to_float128 (ti.matrix[j][k]);
+            }
+        }
+
+        if (pixman_transform_point_f128 (&tf, &vf, &result_f))
+        {
+            if (transform_ok ||
+                (does_it_fit_fixed_48_16 (result_f.v[0]) &&
+                 does_it_fit_fixed_48_16 (result_f.v[1]) &&
+                 does_it_fit_fixed_48_16 (result_f.v[2])))
+            {
+                for (j = 0; j < 3; j++)
+                {
+                    double diff = fabs (result_f.v[j] -
+                                        pixman_fixed_to_float128 (result_i.v[j]));
+
+                    if (is_affine && diff > (0.51 / 65536.0))
+                    {
+                        printf ("%d:%d: bad precision for affine (%.12f)\n",
+                               testnum, i, diff);
+                        abort ();
+                    }
+                    else if (diff > (0.71 / 65536.0))
+                    {
+                        printf ("%d:%d: bad precision for projective (%.12f)\n",
+                               testnum, i, diff);
+                        abort ();
+                    }
+                }
+            }
+        }
+#endif
+    }
+    return crc32;
+}
+
+int
+main (int argc, const char *argv[])
+{
+    return fuzzer_test_main ("matrix", 20000,
+			     0xBEBF98C3,
+			     test_matrix, argc, argv);
+}